The Hypergeometric(f, k) command computes a closed form of the indefinite sum of f with respect to k.

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The following algorithms are used to handle indefinite sums of hypergeometric terms (see the References section):

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Gosper's algorithm,

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Koepf's extension to Gosper's algorithm, and

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the algorithm to compute additive decompositions of hypergeometric terms developed by Abramov and Petkovsek.

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If the option failpoints=true (or just failpoints for short) is specified, then the command returns a pair s&comma;p&comma;q, where s is the closed form of the indefinite sum of f w.r.t. k, as above, and p&comma;q are lists of points where f does not exist or the computed sum s is undefined or improper, respectively (see SumTools[IndefiniteSum][Indefinite] for more detailed help).

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